The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Here's an yet another seamless note paper texture for use as a background on websites.
Source V. Hartikainen
These dots are already worn for you, so you don’t have to.
Source Matt McDaniel
This one is amazing, truly original. Go use it!
Source Viahorizon
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Zero CC tileable Crackled Cement (streaks) texture, photographed and made by me. CC0
Source Sojan Janso
A seamless background pattern with a texture of wood planks. This wood background pattern has vertically arranged planks. You may try to rotate it 90°, to see how it will look like when the wood planks are arranged horizontally.
Source V. Hartikainen
Inspired by a drawing in 'Poems', James Smith, 1881.
Source Firkin